Various forms of tapering borers or tapering reamers are known, a typical example of which comprises cutting portions which with their cutting edges define a tapering or conical generated surface when the tool is rotated about its longitudinal centre line. Between the cutting portions the tool has chip-receiving grooves, the cutting portions and the grooves extending in alternate relationship around the periphery of the tool. Each cutting portion comprises a cutting face and a relief face intersecting at the cutting edge. Each cutting portion may further include; a round grinding portion or "margin" adjoining the cutting edge. Together the cutting face and relief face define a wedge angle which is also known as the tool angle. The cutting face defines a rake angel, with respect to a first reference plane which extends through the longitudinal axis of the tool and the corresponding cutting edge, while the relief face defines a relief angle with respect to a second reference plane which is normal to the first reference plane and which extends through the respective cutting edge of the cutting portion.
In such tools the relief angle is constant along the longitudinal axis of the tool. In such a tool design the relief angle is fixed at the smallest diameter of the tool, that is to say the smallest diameter of the tapering generated surface formed by the rotational movement of the cutting edges of the cutting portions as the tool is rotated, for the reason that, as a result of the extent of the relief surface, the relief angle in that part of the tool cannot fall below a given value without adversely affecting the removal of chips from a workpiece to be machined. Then, as a result of the relief angle being constant over the entire length of the tool, at any diameter along the length of the tool which is larger than the above-mentioned minimum diameter, the tool has a relief face which is spaced from the generated surface referred to above. The distance between the generated surface and the relief face progressively increases, in proportion to the increase in the diameter of the generated surface in comparison with the above-mentioned minimum diameter thereof. Thus, as the diameter of the tapering generated surface increases, the space between that surface and the relief face of the tool becomes larger and larger in a completely unnecessary fashion. On the other hand, with a given wedge or tool angle in respect of the or each cutting portion, the rake angle of the or each cutting portion is fixed by virtue of the relief angle so that in the tapering tools of the above-discussed kind, with a constant relief angle, the rake angle also remains constant along each cutting portion if each cutting portion has a constant tool angle along its longitudinal extent. A constant tool angle for each cutting portion is generally desirable and is the conventional practice because it is only in that way that it is possible to provide for uniformity of wear of the cutting portions. Consequently, in the known tools in the form of tapering borers or tapering reamers, the rake angle is independent of the respective diameter of the tapering generated surface of the tool, and remains of the same magnitude. The result of that design configuration however is that the removal of chip material from the workpiece to be machined and the flow of chip material is the same over the entire length of the tapering tool.